A discussion about stabilizing periodic and near-periodic switching signals

A rather natural way to address the stabilizability problem for switched systems is to make use of periodic switching laws. The success is guaranteed, provided that the discrete dynamical system associated to the periodic law is stable.In this paper we discuss a more general type of stabilizing switching laws, called near-periodic, which can be implemented when the associated discrete dynamical system has a non-trivial stable submanifold, and a suitable controllability condition is fulfilled.